My bf's ex now says the baby is his after first saying that it wasn't and she moved away not telling him about anything concerning the baby(now 4mnths old). There is a chance it could be he's but didn't know because she slept with many guys. She has drugs and alcohol around the child and if the paternity test proves he is the father, is there a chance he could get custody of the child based on the best interest of the child?

If he is the father he stands a good chance getting custody in the best interest of the child .
Now days many fathers are getting custody of their kids although if tests show he is not the father he should report her to the proper authorities for the safety and well being of the child.

I thought the same as well thank you that is comforting.

You are more than welcome